Author
Topic: Is infinity an illusion? (Read 68730 times)

lean bean

Do you mean there may be other universes in which things could happen that cannot happen in our Universe, or do you have concrete examples?

To give a quote from John Barrow's book 'The Infinite Book' page 197....The bubbles are universes .

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As in the chaotic inflationary process, each of the bubbles may carry a different number of forces of Nature,different vaues for some (or even all) constants of Nature,and different numbers of dimensions of space and time.

Same page

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if it is infinite in size, without us having to appeal to metaphysical notions like 'other' universes existing in parallel realities. One infinite universe contains enough room to contain all these possibilities.This is the conserative multiverse option.

His italics

Same book page 192.

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It is this impressive agreement between the simple predictions of the inflationary universe theory and a large number of high-precision observations that provokes us to take seriously the wider consequences of the inflationary universe for infinite universes.

Bill, I don't know why you assume the universe was infinitesimally small to begin with? Just because the equations of running the observable universe backwards ends with those equations breaking down/singularity, Why do you assume that means the whole of the universe was once infinitesimally small?

That's what modern cosmology says so its no surprise that Bill accepts that as it is. I do. Cosmologists and most physicists know that the big bang theory is an extrapolation running back wards. But it works that way. Only when we run things back to 10-34s or so do we see things working out to what we observe today.

pete, are you saying within that 10-34s the universe was infinitesimally small, how do you know the size for certain within the period of undeterminable space and time.

Bill, I don't know why you assume the universe was infinitesimally small to begin with? Just because the equations of running the observable universe backwards ends with those equations breaking down/singularity, Why do you assume that means the whole of the universe was once infinitesimally small?

That's what modern cosmology says so its no surprise that Bill accepts that as it is. I do. Cosmologists and most physicists know that the big bang theory is an extrapolation running back wards. But it works that way. Only when we run things back to 10-34s or so do we see things working out to what we observe today.

pete, are you saying within that 10-34s the universe was infinitesimally small, how do you know the size for certain within the period of undeterminable space and time.[/quote]I can’t recall where I got that from so let’s ignore that comment. I’m not sure what LBs problem was above either. However Infinitely small is not a real term. It has no meaning. And we don’t know what happened at t = 0 and we can’t take the universe back to a size of zero. The term infinite quite literally means unbounded. So the term infinitesimally small means unbounded smallness which is meaningless.

Our understanding of physics today only allows us to run the equations back only so far.

Note: Please understand that when it comes to the early universe and cosmology that I’m a beginner. I do not profess to be an expert or even fully versed.

Let me quote Gravitation and Spacetime – Third Ed. by Ohanian and Ruffini. From Chapter 10 Early Universe page 445

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Entirely new physics needs to be introduced to deal with the behavior of the universe at earlier times, at about 10-32s and earlier, when the universe apparently suffered a quick and very large inflation. Strong circumstantial evidence consistent with such an inflation has now been discovered by analysis of miniscule temperature fluctuations in the observed distribution of the cosmic background radiation over the sky. But the mechanism underlying inflation remains purely conjectural, and a large variety of possible theoretical scenarios are still under investigation.

One of the things that emerges in this thread is the thought that I am basing arguments on unwarranted assumptions. I asked myself the following questions, and made a stab at answering them.

Q1. Given that there is something now; can there ever have been nothing?

A1. Possibly.

Q2. How could that be possible?

A2. Outside our observable universe the laws of physics, including the laws of causality, could be different. It is possible that something could come from nothing as a result of a process unknown in this Universe.

Q3. Is there anything we can observe in our Universe that would point to such differences?

A3. Not to my knowledge.

Q4. Is there anything we can observe in our universe that would negate such differences?

A4. Not to my knowledge.

Q5. If one needs to make an assumption about what conditions might be outside the Universe, is it better to assume that conditions are essentially as we observe them in the Universe, or that that they are different?

A5. Ockham’s razor would tend to point towards the former. Also, James Hutton started a revolution in geology with his assertion that “The present is the key to the past”. One might extrapolate this to “The known is the key to the unknown”.

Q6. How reasonable is it to make assumptions in order to try to move from the known to the unknown?

A6. Science in general, and cosmology in particular, would be severely hampered without a few very basic assumptions.

Cosmologists assume that the Universe is both homogeneous and isotropic, even beyond the horizon of our observations.

The laws of physics are assumed to be the same everywhere in the Universe, including those parts we cannot observe.

Even the second law of thermodynamics is based on an assumption - that the Universe began its life in an ordered state.

Q7. Can anyone make assumptions about the unknown, or should only experts do this?

A7. Obviously, experts are in a better position to make reasonable assumptions than are non-experts. Non-experts would be wise to run their ideas past experts to test validity. However, there is often disagreement among experts, so the extent to which ideas are validated may depend on the choice of expert.

So the term infinitesimally small means unbounded smallness which is meaningless.

This is probably nit-picking, but surely "unbounded smallness" would be the definition of infinitely small; whereas "infinitesimally small" means so small it cannot be measured, but not zero.

Just to be the grumpy dissenter--infinitely small is a bit of an abuse of the term "infinitesimally small" as you noted, Pete, but it does certainly have meaning mathematically. If it didn't, we'd have no calculus!

We can debate whether it has meaning physically in the sense that it may or may not make sense to talk about infinitesimally small regions of space. The Planck length, as I understand it, isn't the smallest possible distance--it's simply where we need a better theory. (That better theory may very well end up telling us that the Planck length is the smallest unit of distance, but we don't have it yet!)

One of the things that emerges in this thread is the thought that I am basing arguments on unwarranted assumptions. I asked myself the following questions, and made a stab at answering them.

...

Q5. If one needs to make an assumption about what conditions might be outside the Universe, is it better to assume that conditions are essentially as we observe them in the Universe, or that that they are different?

A5. Ockham’s razor would tend to point towards the former. Also, James Hutton started a revolution in geology with his assertion that “The present is the key to the past”. One might extrapolate this to “The known is the key to the unknown”.

Q6. How reasonable is it to make assumptions in order to try to move from the known to the unknown?

A6. Science in general, and cosmology in particular, would be severely hampered without a few very basic assumptions.

Cosmologists assume that the Universe is both homogeneous and isotropic, even beyond the horizon of our observations.

The laws of physics are assumed to be the same everywhere in the Universe, including those parts we cannot observe.

Even the second law of thermodynamics is based on an assumption - that the Universe began its life in an ordered state.

Q7. Can anyone make assumptions about the unknown, or should only experts do this?

A7. Obviously, experts are in a better position to make reasonable assumptions than are non-experts. Non-experts would be wise to run their ideas past experts to test validity. However, there is often disagreement among experts, so the extent to which ideas are validated may depend on the choice of expert.

Conclusion: Thinking outside the box is hard work. :)

I thought I responded previously but I can't find it, so maybe I got distracted and forgot to post. (Just got a new puppy, so I tend to get about 30 seconds at a time at the computer before he chews on something he shouldn't!)

In light of what you're saying here, I think my main contention with your argument is your assumption that extrapolation to the unknown is always the best option. It isn't! Extrapolation is fair when you have reason to believe your models are continuously connected to the unknown cases in some way. For example, we observe large-scale homogeneity and isotropy in the visible universe, and we expect the universe as a whole to be a large, connected region of space-time. Therefore, it's reasonable to assume that isotropy and homogeneity hold for the universe as a whole.

Similarly, physical laws seem to be consistent over space and time, so it's natural to assume that the same laws which hold today also also held back near the birth of the universe.

Both of these may be false, but since we can continuously extend our models to cover these regions we don't have access to, it's most natural to assume that this extrapolation holds.

However, when you can't continuously extend your models to cover the new cases, Occam's razor doesn't hold. You're essentially saying "I'm going to apply what I know to an unrelated system." The simplest explanation is not to enforce the unrelated model to hold. I'd argue that the simplest model is to say "I can put bounds on how this system behaves in terms of measurements I've made, but I have to assume I know little about the model at work."

For example, a lot of people mistakenly assume that "photons don't experience time." This is based on erroneously extending special relativity, which says that if a clock moves past a stationary observer, the clock appears to run slowly as measured by the observer. The closer the clock moves to the speed of light, the slower it appears to run. In the limit as it's speed approaches the speed of light, its clock slows down without bound. It's natural to say "well, that observer sees all photons as flying past him at the speed of light, so photons must experience that limiting case and so their clocks don't move at all as measured by that observer." (By the same logic, an observer riding on a photon would see the entire universe as static, since he/she would measure all external clocks as static). This immediately leads to a paradox, since we know photons are emitted an absorbed, interacting at 2 points in time, so clearly they do somehow "experience" time.

The problem here is that special relativity is defined over a set of states (observers moving with constant speeds) that can be connected continuously to each other by accelerations (Lorentz boosts). We've only tested special relativity in a small range of cases, but we can safely extrapolate it to all inertial (constant speed) reference frames because they're all continuously connected to each other within the framework of the theory. However, no amount of Lorentz boosting will take you to the reference frame of light, so this case isn't connected in any way to the rest of the theory, including cases we've tested. There's no justification for extrapolating to this unconnected case and here it provides answers that are both paradoxical and useless (and wrong in the sense that they have no meaning).

I'm arguing throughout that your ideas of finite-sized objects growing at finite rates makes a lot of sense, but only within our universe, since that's where all the examples we know of live. Moreover, finite objects must exist in space, and rates of increase in size occur over time, so we're justified in extrapolating these ideas to any region in space and time that's connected to the region we've observed--in other words, the entire universe (possibly excepting black holes and other singular objects). In other words, these ideas make sense so long as your object is bounded in some region of space and time within our universe.

The problem is that you're asking us to extrapolate this idea to our entire universe, which clearly doesn't live in a region of space and time within itself! Whatever set it's a part of (if it is a part of any larger set) is not in any way we know of continuously connected to the space and time of our universe (since anything connected to our universe would be part of our universe.)

I'd go further and argue that extrapolation is useless when performed to unconnected cases. I'd also suggest that the best way to tackle the problem of an infinite universe is to return the fundamentals of science: can we come up with a theory that makes a testable prediction based on the size of the universe. Then we can apply Occam's razor to boil down these theories to the simplest ones and experiment or observation should then be the judge of which one is best.

Once again, thanks for the detailed response, JP. What you say makes very good sense to me.

I must point out that I didn’t intend saying, or implying, “that extrapolation to the unknown is always the best option”.What I was saying was that if one were speculating about the unknown one would have the choice of assuming that the situation there would be essentially as it is in the known Universe; or that it would be essentially different. Assuming (without a sound reason) that it is different introduces an additional level of “unknown”. This is where I was applying Ockham’s razor.

Correct me if I’m wrong, but you seem to be saying something more like “We don’t know what, if anything, is outside our Universe, so there is no point in trying to think about it.”

That’s a perfectly valid point of view, but, to me it seems much like saying “God created it; end of speculation.” While this may also be a valid point of view, it too seems a bit restrictive.

1) Boiled down, my point is basically that your idea is based on things we view within the space-time of our universe. You're trying to extend this idea to regions outside of our universe, where space and time as we know them probably don't exist. How would you even go about doing this? It seems a bit contrived to try to force our models into a case that's probably completely alien to them just for "simplicity."

2) I wouldn't say it's not worth questioning what's outside the universe, but I would say that as scientists it's our duty to make every possible effort to come up with testable models. This is where much of this does go into the domain of experts (and I'm not an expert on this!) Sure, these models will likely have a lot of speculation, but we should be speculating towards testable answers. I see two possible ways forward on this front: 1) we can work entirely within the universe and try to figure out testable consequences if the universe is finite vs. infinite or 2) we can work on models outside the universe with testable predictions. This second vein of work contains string theory and other similar theories of everything which are generally criticized because they don't provide testable predictions. I also don't find them terribly convincing for that reason. But there are plenty of scientists who are convinced that the theory is heading in the right direction towards testability and I trust them, since I don't know enough of the area to judge otherwise. :p

But hey--you may be right. I just don't think it's the most fruitful way to approach the question.

1) Boiled down, my point is basically that your idea is based on things we view within the space-time of our universe. You're trying to extend this idea to regions outside of our universe, where space and time as we know them probably don't exist. How would you even go about doing this? It seems a bit contrived to try to force our models into a case that's probably completely alien to them just for "simplicity."

I thought that string cosmology was doing something very similar. Is this not the case? They'e using that to formulate the Pre-Big Bang scenario

You're trying to extend this idea to regions outside of our universe, where space and time as we know them probably don't exist.

In this sort of discussion it is easy to divert to side issues which, although relevant to some extent, detract from the main point, or even give a wrong impression.

In fact, the only concept I would seek to apply to anything beyond our Universe is that if there had ever been nothing, there would be nothing now. I certainly have no wish to argue that space and time exist outside the Universe. I would not even join the multiverse advocates in assuming that whatever might be beyond our Universe would need to be composed of universes.

I like the look of the puppy and hope you and he/she have many enjoyable years together.

You're trying to extend this idea to regions outside of our universe, where space and time as we know them probably don't exist.

In this sort of discussion it is easy to divert to side issues which, although relevant to some extent, detract from the main point, or even give a wrong impression.

In fact, the only concept I would seek to apply to anything beyond our Universe is that if there had ever been nothing, there would be nothing now.

That goes to a bigger side issue--what is nothing? Do you mean a complete vacuum, or do you mean "absolute nothing," e.g. no space, time or anything else? (We did have a lengthy argument elsewhere that showed the difficulty in defining absolute nothing.)

Again, it seems like a simple requirement to say "if there ever was nothing, there will be nothing now," but that's far from simple once you step outside the bounds of our universe.

Define "nothing." Define "come from." Keep in mind that we're outside the universe which contains all (known) space and time.

Nothing: Complete absence of anything, known or unknown to us.

I think the result of the previous thread on nothing was that isn't a scientifically useful definition, since science deals with measurable which are necessarily tied to "somethings". If you think "nothing" is scientifically useful, I suspect the burden of proof is on you that it can be so before we start using it to make predictions about the universe.

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Comes from (as used here): Is caused, created or otherwise brought into existence by.

That seems to imply that there was a time at which something didn't exist and a time at which it did, which means there is time outside of the universe. What justification do you have for assuming this, since the universe presumably contains all time? If that's not what you mean, created/caused/brought into existence are problematic to use in a definition, since all imply time passing.

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